Mathematics is the ultimate divisive topic; either one detests completely, inexorably, and passionately, or one is intrigued by the possibilities afforded by the subject. Knitters aren’t immune to this rift; while there are people who can’t calculate the number of stitches needed to cast on a simple hat, there are others like Sarah Marie Bel-Castro, knitter and science geek extraordinaire. I hadn’t heard of Ms. Bel-Castro before coming across her 2013 article in American Scientist, but, as one who has made an uneasy piece with mathematics, I find her inspirational. Why?

Studying late into the night found Bel-Castro falling asleep in her graduate classes; as a knitter, she turned to needles and yarn to help keep herself awake. After creating a few sweaters, she found herself gravitating towards an unusual form of amigurumi; she began to create knitted models of mathematical concepts. Since then, she’s co-authored two books on the subject, and has researched the history of using knitting to better understand what it often an arcane and occult subject.

There is a branch of mathematics called topology, which is the attempt to describe geometric objects that have been pulled or distorted into different shapes. Many knitters are familiar with the idea of a Moebius scarf, where the garment has only one side because of a half-twist; this is one example of topology and of topography, the art of graphing such a shape. Bel-Castro’s interest lies in another topological shape, the Klein bottle. This object is essentially a Moebius strip stretched into the shape of a jug; to make one, a crafter starts with a tube and then bends it until it doubles back into itself. A true Klein bottle exists only in four dimensions, but it is possible to make a 3-D representation. Because it only has one side, a true Klein bottle cannot hold liquid.

For many of us, this kind of phenomenon exists only to satisfy intellectual curiosity; simple calculations are difficult enough that we never find ourself learning higher mathematical concepts. Bel-Castro, however, finds the finished object to be a wonderful teaching aid. In addition, knitting a Klein bottle forces the student to think about an abstract concept, determine the important parts, and then create it in concrete form; thus, the process is an aid to studying.

Klein’s 2003 article notes that knitting has long been used to make topographic models. Her article illustrates the issues that occur when one tries to create a construct of an idea; it’s somewhat akin to the use of metaphors, similes, and symbols in language. I have to be honest here and admit that I understand about seventy-five percent of Bel-Castro’s explanation. However, even that is enough to appreciate this unusual form of knitting and to be interested in reading more. I’ll definitely peruse the bibliography at the end of the article.

Disclaimer: I have not met Sarah Marie Bel-Castro and have no connection with her books or articles. I perused her work on the Internet.

For further reading:

Bel-Castro, Sarah Marie. “Adventures in Mathematical Knitting,” American Scientist, Volume 101, Number 2, March-April 2013. https://www.americanscientist.org/article/adventures-in-mathematical-knitting